Methods and devices for coding and decoding the position of the last significant coefficient

ABSTRACT

Methods and devices are described for entropy coding data using an entropy coder to encode quantized transform domain coefficient data. Last significant coefficient information is signaled in the bitstream using two-dimensional coordinates for the last significant coefficient. The context for bins of one of the coordinates is based, in part, upon the value of the other of the coordinates. In one case, instead of signaling last significant coefficient information, the number of non-zero coefficients is binarized and entropy encoded.

FIELD

The present application generally relates to data compression and, inparticular, to an encoder, a decoder and methods of coding and decodingthe last significant transform coefficient.

BACKGROUND

Data compression, whether lossy or lossless, often uses entropy codingto encode a decorrelated signal as a sequence of bits, i.e. a bitstream.Efficient data compression has a wide range of applications, such asimage, audio, and video encoding. The current state-of-the-art for videoencoding is the ITU-T H.264/MPEG AVC video coding standard. It defines anumber of different profiles for different applications, including theMain profile, Baseline profile and others. A next-generation videoencoding standard is currently under development through a jointinitiative of MPEG-ITU: High Efficiency Video Coding (HEVC).

There are a number of standards for encoding/decoding images and videos,including H.264, that employ lossy compression processes to producebinary data. For example, H.264 includes a prediction operation toobtain residual data, followed by a DCT transform and quantization ofthe DCT coefficients. The resulting data, including quantizedcoefficients, motion vectors, coding mode, and other related data, isthen entropy coded to generate a bitstream of data for transmission orstorage on a computer-readable medium. It is expected that HEVC willalso have these features.

A number of coding schemes have been developed to encode binary data.For example, JPEG images may be encoded using Huffman codes. The H.264standard allows for two possible entropy coding processes: ContextAdaptive Variable Length Coding (CAVLC) or Context Adaptive BinaryArithmetic Coding (CABAC). CABAC results in greater compression thanCAVLC, but CABAC is more computationally demanding. In any of thesecases, the coding scheme operates upon the binary data to produce aserial bitstream of encoded data. At the decoder, the decoding schemereceives the bitstream and entropy decodes the serial bitstream toreconstruct the binary data.

It would be advantageous to provide for an improved encoder, decoder andmethod of entropy coding and decoding.

BRIEF DESCRIPTION OF THE DRAWINGS

Reference will now be made, by way of example, to the accompanyingdrawings which show example embodiments of the present application, andin which:

FIG. 1 shows, in block diagram form, an encoder for encoding video;

FIG. 2 shows, in block diagram form, a decoder for decoding video;

FIG. 3 shows a block diagram of an encoding process;

FIG. 4 shows a simplified block diagram of an example embodiment of anencoder;

FIG. 5 shows a simplified block diagram of an example embodiment of adecoder;

FIG. 6 illustrates a zig-zag coding order for a 4×4 block ofcoefficients;

FIG. 7 diagrammatically shows a portion of a bitstream;

FIG. 8 shows, in flowchart form, an example method of entropy encodinglast significant coefficient information;

FIG. 9 shows, in flowchart form, an example method of entropy decoding abitstream of encoded data to reconstruct quantized transform domaincoefficient data;

FIG. 10 shows, in flowchart form, an example method of encoding asignificance map; and

FIG. 11 shows an anti-diagonal grouping of coefficients in a 4×4 block.

Similar reference numerals may have been used in different figures todenote similar components.

DESCRIPTION OF EXAMPLE EMBODIMENTS

The present application describes devices, methods and processes forencoding and decoding binary data. In particular, the presentapplication describes methods and devices for coding and decoding thelast significant coefficient position in a block-based coding scheme.

In one aspect, the present application describes a method for encodingquantized transform domain coefficient data including last significantcoefficient information. The method includes binarizing each of twopositions of two-dimensional coordinates of the last significantcoefficient; determining a context for each bin of one of the positions;determining a context for each bin of the other of the positions,wherein the context of each bin of the other of the positions is based,in part, upon said one of the positions; and entropy encoding thebinarized positions based upon the context determined for each of thebins of the binarized positions to produce encoded data.

In another aspect, the present application describes method for decodinga bitstream of encoded data to reconstruct quantized transform domaincoefficient data. The method includes entropy decoding a portion of theencoded data to produce two binarized positions defining two-dimensionalcoordinates of a last significant coefficient, wherein entropy decodingthe portion of the data includes determining a context for each bin ofone of the positions, and determining a context for each bin of theother of the positions, wherein the context of each bin of the other ofthe positions is based, in part, upon said one of the positions; entropydecoding a significant coefficient sequence based upon thetwo-dimensional coordinates of the last significant coefficient; entropydecoding level information based upon the significant coefficientsequence; and reconstructing the quantized transform domain coefficientdata using the level information and the significant coefficientsequence.

In yet a further aspect, the present application describescomputer-readable media storing computer-executable program instructionswhich, when executed, configured a processor to perform the describedmethods of encoding and/or decoding.

Other aspects and features of the present application will be understoodby those of ordinary skill in the art from a review of the followingdescription of examples in conjunction with the accompanying figures.

The following description relates to data compression in general and, inparticular, to the efficient encoding and decoding of finite alphabetsources, such as a binary source. In many of the examples given below,particular applications of such an encoding and decoding scheme aregiven. For example, many of the illustrations below make reference tovideo coding. It will be appreciated that the present application is notnecessarily limited to video coding or image coding. It may beapplicable to the any type of data subject to a context-based encodingscheme of data that is block-based and that involves signaling theposition of the last significant bit or symbol in the block.

The example embodiments described herein relate to data compression of afinite alphabet source. Accordingly, the description often makesreference to “symbols”, which are the elements of the alphabet. In somecases, the description herein refers to binary sources, and refers tothe symbols as bits. At times, the terms “symbol” and “bit” may be usedinterchangeably for a given example. It will be appreciated that abinary source is but one example of a finite alphabet source. Thepresent application is not limited to binary sources.

In the description that follows, example embodiments are described withreference to the H.264 standard. Those ordinarily skilled in the artwill understand that the present application is not limited to H.264 butmay be applicable to other video coding/decoding standards, includingpossible future standards, such as HEVC. It will also be appreciatedthat the present application is not necessarily limited to videocoding/decoding and may be applicable to coding/decoding of any finitealphabet sources.

Reference is now made to FIG. 1, which shows, in block diagram form, anencoder 10 for encoding video. Reference is also made to FIG. 2, whichshows a block diagram of a decoder 50 for decoding video. It will beappreciated that the encoder 10 and decoder 50 described herein may eachbe implemented on an application-specific or general purpose computingdevice, containing one or more processing elements and memory. Theoperations performed by the encoder 10 or decoder 50, as the case maybe, may be implemented by way of application-specific integratedcircuit, for example, or by way of stored program instructionsexecutable by a general purpose processor. The device may includeadditional software, including, for example, an operating system forcontrolling basic device functions. The range of devices and platformswithin which the encoder 10 or decoder 50 may be implemented will beappreciated by those ordinarily skilled in the art having regard to thefollowing description.

The encoder 10 receives a video source 12 and produces an encodedbitstream 14. The decoder 50 receives the encoded bitstream 14 andoutputs a decoded video frame 16. The encoder 10 and decoder 50 may beconfigured to operate in conformance with a number of video compressionstandards. For example, the encoder 10 and decoder 50 may be H.264/AVCcompliant. In other embodiments, the encoder 10 and decoder 50 mayconform to other video compression standards, including evolutions ofthe H.264/AVC standard, such as HEVC.

The encoder 10 includes a spatial predictor 21, a coding mode selector20, transform processor 22, quantizer 24, and entropy coder 26. As willbe appreciated by those ordinarily skilled in the art, the coding modeselector 20 determines the appropriate coding mode for the video source,for example whether the subject frame/slice is of I, P, or B type, andwhether particular macroblocks (or coding units) within the frame/sliceare inter or intra coded. The transform processor 22 performs atransform upon the spatial domain data. In particular, the transformprocessor 22 applies a block-based transform to convert spatial domaindata to spectral components. For example, in many embodiments a discretecosine transform (DCT) is used. Other transforms, such as a discretesine transform or others may be used in some instances. Applying theblock-based transform to a block of pixel data results in a set oftransform domain coefficients. The set of transform domain coefficientsis quantized by the quantizer 24. The quantized coefficients andassociated information, such as motion vectors, quantization parameters,etc., are then encoded by the entropy coder 26.

Intra-coded frames/slices (i.e. type I) are encoded without reference toother frames/slices. In other words, they do not employ temporalprediction. However intra-coded frames do rely upon spatial predictionwithin the frame/slice, as illustrated in FIG. 1 by the spatialpredictor 21. That is, when encoding a particular block the data in theblock may be compared to the data of nearby pixels within blocks alreadyencoded for that frame/slice. Using a prediction algorithm, the sourcedata of the block may be converted to residual data. The transformprocessor 22 then encodes the residual data. H.264, for example,prescribes nine spatial prediction modes for 4×4 transform blocks. Insome embodiments, each of the nine modes may be used to independentlyprocess a block, and then rate-distortion optimization is used to selectthe best mode.

The H.264 standard also prescribes the use of motionprediction/compensation to take advantage of temporal prediction.Accordingly, the encoder 10 has a feedback loop that includes ade-quantizer 28, inverse transform processor 30, and deblockingprocessor 32. These elements mirror the decoding process implemented bythe decoder 50 to reproduce the frame/slice. A frame store 34 is used tostore the reproduced frames. In this manner, the motion prediction isbased on what will be the reconstructed frames at the decoder 50 and noton the original frames, which may differ from the reconstructed framesdue to the lossy compression involved in encoding/decoding. A motionpredictor 36 uses the frames/slices stored in the frame store 34 assource frames/slices for comparison to a current frame for the purposeof identifying similar blocks. Accordingly, for macroblocks to whichmotion prediction is applied, the “source data” which the transformprocessor 22 encodes is the residual data that comes out of the motionprediction process. The residual data is pixel data that represents thedifferences (if any) between the reference block and the current block.Information regarding the reference frame and/or motion vector may notbe processed by the transform processor 22 and/or quantizer 24, butinstead may be supplied to the entropy coder 26 for encoding as part ofthe bitstream along with the quantized coefficients.

Those ordinarily skilled in the art will appreciate the details andpossible variations for implementing H.264 encoders.

The decoder 50 includes an entropy decoder 52, dequantizer 54, inversetransform processor 56, spatial compensator 57, and deblocking processor60. A frame buffer 58 supplies reconstructed frames for use by a motioncompensator 62 in applying motion compensation. The spatial compensator57 represents the operation of recovering the video data for aparticular intra-coded block from a previously decoded block.

The bitstream 14 is received and decoded by the entropy decoder 52 torecover the quantized coefficients. Side information may also berecovered during the entropy decoding process, some of which may besupplied to the motion compensation loop for use in motion compensation,if applicable. For example, the entropy decoder 52 may recover motionvectors and/or reference frame information for inter-coded macroblocks.

The quantized coefficients are then dequantized by the dequantizer 54 toproduce the transform domain coefficients, which are then subjected toan inverse transform by the inverse transform processor 56 to recreatethe “video data”. It will be appreciated that, in some cases, such aswith an intra-coded macroblock, the recreated “video data” is theresidual data for use in spatial compensation relative to a previouslydecoded block within the frame. The spatial compensator 57 generates thevideo data from the residual data and pixel data from a previouslydecoded block. In other cases, such as inter-coded macroblocks, therecreated “video data” from the inverse transform processor 56 is theresidual data for use in motion compensation relative to a referenceblock from a different frame. Both spatial and motion compensation maybe referred to herein as “prediction operations”.

The motion compensator 62 locates a reference block within the framebuffer 58 specified for a particular inter-coded macroblock. It does sobased on the reference frame information and motion vector specified forthe inter-coded macroblock. It then supplies the reference block pixeldata for combination with the residual data to arrive at the recreatedvideo data for that macroblock.

A deblocking process may then be applied to a reconstructed frame/slice,as indicated by the deblocking processor 60. After deblocking, theframe/slice is output as the decoded video frame 16, for example fordisplay on a display device. It will be understood that the videoplayback machine, such as a computer, set-top box, DVD or Blu-Rayplayer, and/or mobile handheld device, may buffer decoded frames in amemory prior to display on an output device.

Entropy coding is a fundamental part of all lossless and lossycompression schemes, including the video compression described above.The purpose of entropy coding is to represent a presumably decorrelatedsignal, often modeled by an independent, but not identically distributedprocess, as a sequence of bits. The technique used to achieve this mustnot depend on how the decorrelated signal was generated, but may relyupon relevant probability estimations for each upcoming symbol.

There are two common approaches for entropy coding used in practice: thefirst one is variable-length coding, which identifies input symbols orinput sequences by codewords, and the second one is range (orarithmetic) coding, which encapsulates a sequence of subintervals of the[0, 1) interval, to arrive at a single interval, from which the originalsequence can be reconstructed using the probability distributions thatdefined those intervals. Typically, range coding methods tend to offerbetter compression, while VLC methods have the potential to be faster.In either case, the symbols of the input sequence are from a finitealphabet.

A special case of entropy coding is when the input alphabet isrestricted to binary symbols. Here VLC schemes must group input symbolstogether to have any potential for compression, but since theprobability distribution can change after each bit, efficient codeconstruction is difficult. Accordingly, range encoding is considered tohave greater compression due to its greater flexibility, but practicalapplications are hindered by the higher computational requirements ofarithmetic codes.

A common challenge for both of these encoding approaches is that theyare serial in nature. In some important practical applications, such ashigh-quality video decoding, the entropy decoder has to reach very highoutput speed, which can pose a problem for devices with limitedprocessing power or speed.

One of the techniques used together with some entropy coding schemes,such as CAVLC and CABAC, both of which are used in H.264/AVC, is contextmodeling. With context modeling, each bit of the input sequence has acontext, where the context may be given by a certain subset of the otherbits, such as the bits that preceded it, or side information, or both.In a first-order context model, the context may depend entirely upon theprevious bit (symbol). In many cases, the context models may beadaptive, such that the probabilities associated with symbols for agiven context may change as further bits of the sequence are processed.In yet other cases, the context of a given bit may depend upon itsposition in the sequence, e.g. the position or ordinal of a coefficientin a matrix or block of coefficients.

Reference is made to FIG. 3, which shows a block diagram of an exampleencoding process 100. The encoding process 100 includes a contextmodeling component 104 and an entropy coder 106. The context modelingcomponent 104 receives the input sequence x 102, which in this exampleis a bit sequence (b₀, b₁, . . . , b_(n)). In this example illustration,the context modeling component 104 determines a context for each bitb_(i), perhaps based on one or more previous bits in the sequence orbased on side information, and determines, based on the context, aprobability p_(i) associated with that bit b_(i), where the probabilityis the probability that the bit will be the Least Probable Symbol (LPS).The LPS may be “0” or “1” in a binary embodiment, depending on theconvention or application. The determination of the probability mayitself depend upon the previous bits/symbols for that same context.

The context modeling component outputs the input sequence, i.e. the bits(b₀, b₁, . . . , b_(n)) along with their respective probabilities (p₀,p₁, . . . , p_(n)). The probabilities are an estimated probabilitydetermined by the context model. This data is then input to the entropycoder 106, which encodes the input sequence using the probabilityinformation. For example, the entropy coder 106 may be a binaryarithmetic coder. The entropy coder 106 outputs a bitstream 108 ofencoded data.

It will be appreciated each bit of the input sequence is processedserially to update the context model, and the serial bits andprobability information are supplied to the entropy coder 106, whichthen serially entropy codes the bits to create the bitstream 108. Thoseordinarily skilled in the art will appreciate that, in some embodiments,explicit probability information may not be passed from the contextmodeling component 104 to the entropy coder 106; rather, in someinstances, for each bit the context modeling component 104 may send theentropy coder 106 an index or other indicator that reflects theprobability estimation made by the context modeling component 104 basedon the context model and the current context of the input sequence 102.The index or other indicator is indicative of the probability estimateassociated with its corresponding bit.

In some embodiments, the entropy coder 106 may have a parallelprocessing architecture for encoding the input sequence 102. In such anembodiment, the entropy coder 106 may include a plurality of entropycoders each processing a portion of the input sequence 102. In somecases, the input sequence may be demultiplexed and allocated amongst theparallel entropy coders on the basis of the estimated probabilitiesassociated with the respective bits. In other words, a bit from theinput sequence 102 is allocated to one of the parallel entropy coders onthe basis of its estimated probability.

At the decoder, the encoded bitstream is decoded using a reverseprocess. In particular, the decoder performs the same context modelingand probability estimation process to determine the context of the nextreconstructed symbol of the reconstructed sequence. On the basis of thecontext determined for the next reconstructed symbol, an estimatedprobability is determined. The encoded bitstream, which may be made upof codewords output by the entropy coder(s), is decoded to obtaindecoded symbols. The determination of context/probability is interleavedwith the decoding of codewords to obtain decoded symbols correspondingto those estimate probabilities.

In a parallel encoding embodiment, the decoder may be configured todemultiplex the encoded bitstream into a plurality of decodedsubsequences, each associated with an estimated probability. The contextmodeling and probability estimation then results in selection of areconstructed symbol from the associated decode subsequence. It will beappreciated that in such an implementation the decoding of the encodedbitstream may be considered de-interleaved from the context modeling andprobability estimation.

It will be appreciated from the detailed description below that thepresent application is applicable to either serial or parallel entropycoding and decoding.

The present application proposes an encoding and decoding process inwhich the last significant coefficient position is encoded and in whichthe context of one of the axes of the position is dependent upon theother axis.

The examples below may refer specifically to video encoding and, inparticular, to the encoding of the sequences sig[i,j] and last[i,j]defined in CABAC as specified in the ITU-T H.264/AVC standard. It willbe appreciated that the present application is not limited to theencoding and decoding of these two specific sequences within CABAC; noris it limited to video encoding and decoding or to the H.264/AVCstandard. The present application describes encoding and decodingmethods and processes that may be applied to other data sequences,including video, image, and, in some instances, audio. The methods andprocesses herein are applicable to encoding and decoding processes thatinvolve a context model which encodes last significant coefficientposition and in which the position is, or can be modeled as,two-dimensional. The examples below may refer to a binary source as anexample, although the present application is more generally applicableto any finite alphabet source.

As described above, example video and image encoding and decodingprocesses employ a block-based transform to convert residual data fromthe pixel domain to the transform domain. Example block-based transformsare a 4×4 DCT or 8×8 DCT. Other sizes or types of transforms (DST orDFT, etc.) may be used in some applications. The matrix or set oftransform data is then quantized by a quantizer to produce a matrix orset of quantized transform domain coefficients. The present applicationmay refer to the matrix of quantized transform domain coefficients as amatrix, a set, or a block, meaning an ordered set of data in which theposition of any one of the coefficients may be specified bytwo-dimensional coordinates: [x,y].

The entropy encoding of the block of quantized transform domaincoefficients is based upon a context model. For example, in H.264/AVC,the block is entropy encoded by first encoding a significance map. Thesignificance map includes two sequences: last [i,j] and sig[i,j]. Thesequence sig[i,j] is a binary sequence indicating whether there is anon-zero coefficient in each position in the DCT block. The othersequence last[i,j] is a binary sequence mapped to the non-zerocoefficients of the DCT block and indicating whether that non-zerocoefficient is the last non-zero coefficient of the DCT block (in thezig-zag scanning order used in H.264 and other transform domain image orvideo encoding schemes). It should be noted that the indices [i,j] arenot two-dimensional coordinate positions in the block; the index i is anindex to the block and the index j is an index to the one-dimensionalcoefficient position in the zig-zag scanning order described below.

The H.264 standard specifies a zig-zag scanning order, for encoding thecoefficients of a DCT block. Referring to a 4×4 DCT block for example,the H.264 standard encodes the 16 coefficients in the zig-zag orderillustrated in FIG. 6. As shown in FIG. 6, the scanning order begins inthe upper left corner of the block and follows a zig-zag pattern to thelower right corner. Once arranged in this coding order, the resultingsequence of coefficients for the i^(th) block is X(i, 0), . . . , X(i,15).

The H.264/AVC standard uses a scheme in which the blocks are encoded insequence. In other words, each sequence X(i, 0), . . . , X(i, 15) isencoded in turn. The context model used in H.264/AVC includesdetermining the two binary sequences, sig[i,j] and last[i, j], for eachvector X[i,j]. The actual values of the coefficients, referred to aslevels, are then also encoded.

To illustrate by example, consider the following example coefficientsequences X:

3, 5, 2, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0  i = 06, 4, 0, 3, 3, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0  i = 14, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0  i = 2

The sequences sig[i,j] and last[i,j] for these coefficient sequences areas follows:

sig[0, j] = 1, 1, 1, 0, 1, 1, 0, 1 last[0, j] = 0, 0, 0, 0, 0, 1sig[1, j] = 1, 1, 0, 1, 1, 0, 1 last[1, j] = 0, 0, 0, 0, 1sig[2, j] = 1, 1, 0, 0, 1 last[2, j] = 0, 0, 1

It will be appreciated that the last[i,j] sequence only includes valueswhen the sig[i,j] is non-zero, and both sequences terminate after thelast non-zero coefficient. Accordingly, last[i,j] will not necessarilyinclude a bit for every bit j in sig[i,j]. It will be appreciated thatthe lengths of these sequences may vary depending on the coefficientvalues. Finally, it will be appreciated that if one knows whether thesig[i,j] sequence contains a non-zero bit, then one will know whetherthere is a corresponding bit in the last[i,j] sequence or not, meaningthe encoding and decoding of these sequences is interleaved by bitposition.

In the H.264/AVC example the probability (sometimes termed “state”) fora bit is determined based on its context. Specifically, the bit historyfor that same context determines the probability that is selected orassigned to that bit. For example, for a bit in the j^(th) position in agiven sequence i, its probability is selected from amongst the 64possible probabilities based on the history of bits in the j^(th)position in previous sequences (i-1, etc.).

As described above, the bits are encoded based upon their probabilities.In some example embodiments, parallel encoding may be used and, in someinstances, the parallel encoding may include an entropy coder specificto each probability. In other example embodiments, serial entropyencoding may be used. In either case, the entropy coder encodes symbolsbased on their associated probabilities.

At the decoder, the same context modeling and probability estimationoccurs in reconstructing the sequence. The probability estimation isused to decode the encoded bitstream to obtain reconstructed symbols.Symbols are selected from the decoded portions of the encoded bitstreamand interleaved to form the reconstructed sequence of symbols on thebasis of their associated probabilities and the context model.

The syntax for a residual block in H.264/AVC using CABAC, is set out inthe table below:

TABLE 1 De- residual_block_cabac( coeffLevel, scrip- startIdx, endIdx,maxNumCoeff ) { tor  if( maxNumCoeff != 64 || ChromaArrayType = = 3 )ae(v)   coded_block_flag ae(v)  for( i = 0; i < maxNumCoeff; i++ )  coeffLevel[ i ] = 0  if( coded_block_flag ) {   numCoeff = endIdx + 1  i = startIdx   while( i < numCoeff − 1 ) {    significant_coeff_flag[i ] ae(v)    if( significant_coeff_flag[ i ] ) {    last_significant_coeff_flag[ i ] ae(v)     if(last_significant_coeff_flag[ i ] )      numCoeff = i + 1    }    i++   }  coeff_abs_level_minus1[ numCoeff − 1 ] ae(v)   coeff_sign_flag[numCoeff − 1 ] ae(v)   coeffLevel[ numCoeff − 1 ] =    (coeff_abs_level_minus1[ numCoeff − 1 ] + 1 ) *    ( 1 − 2 *coeff_sign_flag[ numCoeff − 1 ] )   for( i = numCoeff − 2; i >=startIdx; i− − )    if( significant_coeff_flag[ i ] ) {    coeff_abs_level_minus1[ i ] ae(v)     coeff_sign_flag[ i ] ae(v)    coeffLevel[ i ] = ( coeff_abs_level_minus1[ i ] + 1 ) *            (1 − 2 * coeff_sign_flag[ i ] )    }  } }

The above table provides pseudocode for entropy decoding a bitstreamcontaining sig[i,j], last[i,j] and level information. The descriptor“ae(v)” indicates the entropy decoding of bits from the bitstream toobtain the values indicated in that row in the table.

It will be noted that the bits of sig[i,j] and last[i,j] are interleavedin this syntax. For example, the “if(coded_block_flag)” loop containsthe decoding of a bit from the sig[i,j] sequence (referred to assignificant_coeff_flag[i]) followed by decoding of a bit from thelast[i,j] sequence (referred to as last_significant_coeff_flag[i]) ifthe significant_coeff_flag[i] bit was non-zero.

It will also be appreciated that this syntax relies upon a sequence tosignal the one-dimensional position of the last significant coefficientin the zig-zag scan order for the block.

In accordance with one aspect of the present application, the syntax ismodified to signal the two-dimensional coordinates of the lastsignificant coefficient within the block. For example, in a 4×4 block,the position of the last significant coefficient has x-andy-coordinates, where x and y range between 0 and 3. This coordinate pairmay be communicated in the syntax in place of the last[i,j] sequence.

The question that arises is how to efficiently and effective code thetwo-dimensional coordinates of the last significant coefficient. Afurther question is whether modifications to the context model should bemade for the encoding of this parameter.

In accordance with an aspect of the present application, thetwo-dimensional coordinates are encoded in turn, with the value of thefirst coordinate being partly used to determine the context for encodingthe second coordinate. This concept is based on there being a certaindegree of correlation between the values of two coordinates in the pair,as has been observed empirically. The value of an x-coordinate tends tohave a material impact on the probability of the values for thecorresponding y-coordinate. This relationship can be exploited toimprove the efficiency of the encoding.

In one embodiment in accordance with an aspect of the presentapplication, fixed length codes are used to binarize the x-coordinateand y-coordinate values. Other binarization schemes may be used in otherembodiments.

In accordance with another aspect of the present application, the syntaxfor encoding residual blocks is further modified to include a flag forsignaling that the last significant coefficient is the DC coefficient at[0,0]. This is not an uncommon occurrence in practical implementationsand when this situation is signaled in the bitstream, the bitstream mayforego including the x- and y-coordinate values for the last significantcoefficient in those situations, thereby improving compressionefficiency.

In the description herein, the term “position” may at times be used torefer to the x-coordinate or y-coordinate, as the case may be.

Although example embodiments described below specify that the contextfor encoding the bits of the y-position are dependent, in part, upon thevalue of the x-position, the order is arbitrary. In another embodiment,the context for encoding the x-position may be dependent, in part, uponthe value of the y-position.

One example embodiment of the syntax for encoding a residual block inaccordance with an aspect of the present application is set out in thetable below:

TABLE 2 De- residual_block_cabac( coeffLevel, scrip- startIdx, endIdx,maxNumCoeff ) { tor  if( maxNumCoeff != 64 || ChromaArrayType = = 3 )ae(v)   coded_block_flag ae(v)  for( i = 0; i < maxNumCoeff; i++ )  coeffLevel[ i ] = 0  if( coded_block_flag ) {   numCoeff = endIdx + 1  i = startIdx   last_pos_x = 0   last_pos_y = 0   last_0_flag ae(v)  if( !last_0_flag ) {    last_pos_x ae(v)    last_pos_y ae(v)    if(last_pos_x == 0 )     last_pos_y++   }   last_significant_coeff_flag = 0  while( i < numCoeff − 1 ) {    (pos_x, pos_y) = zigzagTable[i]    if(pos_x == last_pos_x && pos_y == last_pos_y ) {    last_significant_coeff_flag = 1     numCoeff = i + 1    }    if(!last_significant_coeff_flag )     significant_coeff_flag[ i ] ae(v)   i++   }   coeff_abs_level_minus1[ numCoeff − 1 ] ae(v)  coeff_sign_flag[ numCoeff − 1 ] ae(v)   coeffLevel[ numCoeff − 1 ] =   ( coeff_abs_level_minus1[ numCoeff − 1 ] + 1 ) *    ( 1 − 2 *coeff_sign_flag[ numCoeff − 1 ] )   for( i = numCoeff − 2; i >=startIdx; i− − )    if( significant_coeff_flag[ i ] ) {    coeff_abs_level_minus1[ i ] ae(v)     coeff_sign_flag[ i ] ae(v)    coeffLevel[ i ] = ( coeff_abs_level_minus1[ i ] + 1 ) *            (1 − 2 * coeff_sign_flag[ i ] )    }  } }

From the above pseudocode, it will be noted that the decoder initializesvalues for the x-position (last_pos_x=0) and the y-position(last_pos_y=0) and then reads the flag for signaling that the lastsignificant coefficient is the DC coefficient (last_(—)0_flag). The loopimmediately afterwards is only performed if the last_(—)0_flag does notindicate that the last significant coefficient is at [0,0]. In thatcase, the decoder then reads the values for last_pos_x and last_pos_yfrom the bitstream.

It will also be noted that in this embodiment if the last_pos_x value is0, then the y-position is encoded as its value decremented by 1, sincewe know the two-dimensional position in that situation cannot be [0,0]due to the flag setting, so the y-position must be 1 or higher. Becauseof this encoding syntax, if last_pos_x is set to 0 then the value forlast_pos—y is incremented by 1 to restore it to its actual value.Decrementing last_pos_y by 1 for the purpose of encoding in thisspecific situation is for efficiency purposes in the entropy encoding.

After the two-dimensional coordinates have been read, then the decodergoes on to read the significant_coeff_flag[i] sequence from thebitstream. The index [i] sets the current pos_x and pos_y values using azigzag table for mapping the index to coordinate positions. When thepos_x and pos_y values match the last_pos_x and last_pos_y values,respectively, then the last_significant_coeff_flag is set so as to stopthe reading of the sig[i,j] sequence, which is read bit-by-bit assignificant_coeff_flag[i].

Reference is now made to FIG. 7, which diagrammatically illustrates thestructure of the bitstream 200 created in accordance with an aspect ofthe present application. The portion of the bitstream 200 illustrated inFIG. 7, shows data relating to a residual block. The portion of thebitstream 200 as shown is the bitstream before entropy encoding or afterentropy decoding. The entropy encoding may include CABAC, CAVLC, orother context-based entropy coding schemes.

The leading flag is the coded_block_flag. This flag is followed by thelast_(—)0_flag for signaling last significant coefficient coordinates of[0,0]. Then, presuming that the last_(—)0_flag is not set, the bitstream200 includes the last_pos_x and last_pos_y values. Following those isthe sig[i,j] sequence, i.e. the significant coefficients sequence.Finally, the portion of the bitstream 200 includes level information. Itwill be understood that in cases where the last_(—)0_flag is set, thenthe last_pos_x, last_pos_y, and significant coefficients sequence areomitted.

In one embodiment, the last_pos_x and last_pos_y values are binarizedusing fixed-length binarization. The length of these binary values isdependent upon the size of the transform matrix, i.e. the size of theblock of quantized transform domain coefficients.

Reference is now made to FIG. 8, which shows an example method 300 forencoding last significant coefficient data when encoding a residualblock. The example method 300 includes an operation 302 of determiningthe last significant coefficient coordinates. These coordinates may bex- and y-coordinates ranging from 0 to N−1, for an N×N transform blocksize. The coordinates may be referred to as an x-position and ay-position.

In operation 304, the two positions are binarized. As noted above, thepositions may be binarized using a fixed-length binarization. The lengthof the binarized position may be Log₂(N). Other binarization schemes maybe used in other embodiments.

The entropy encoding of the binarized positions involves determining acontext for each bin of the binarized positions. Accordingly, inoperation 306, the context for each bin of one of the positions isdetermined. For the purpose of an example embodiment, the x-position maybe considered the first position to be encoded. The context for each binof the binarized x-position may be based upon a number of factors. Forexample, in one embodiment the context of each bin of the x-position maybe based upon the size of the transform matrix. Previous bins of thex-position (if any) may also impact the context for subsequent bins ofthat x-position.

In operation 308, the context for each bin of the other one of thepositions (in this example, the y-position) is then determined. Indetermining the context for bins of the y-position, the context ispartly dependent upon the value of the x-position. The context for binsof the y-position may also be partly dependent upon the size of thetransform matrix and previous bins (if any) in the y-position.

In operation 310, the binarized positions are then entropy encoded inaccordance with their associated contexts as determined in steps 306 and308. The entropy encoding may include CABAC, CAVLC, or any othersuitable context-based entropy encoding scheme.

Reference will now be made to FIG. 9, which shows a flowchart depictinga method 400 for decoding a bitstream of encoded data to reconstructquantized transform domain coefficient data. The example method 400illustrated in FIG. 9 involves processing a bitstream of encoded datausing a syntax similar to that described herein. In operation 402, aportion of the bitstream is entropy decoded to recover the two binarizedpositions that define the two-dimensional coordinates for the lastsignificant coefficient. This operation includes determining a contextfor each bin of a first one of the positions (for example, thex-position in one embodiment). That context may depend upon, forexample, the size of the transform matrix and previously decoded bins ofthe x-position, if any. Based upon the context for each bin, and thusthe associated estimated probability, entropy decoding of the bitstreamdetermines that bin, which results in reconstructing the binarizedx-position.

Operation 402 further includes determining the context of each bin ofthe other position (the y-position in this example). The context of eachbin of the y-position may depend upon the size of the transform matrixand previous bins of the y-position, if any, but it further depends uponthe value of the x-position. Entropy decoding of the bitstream inaccordance with the determined context for each bin and its consequentestimated probability, results in reconstruction of the binarizedy-position.

In operation 404, the x-position and y-position are used to entropydecode the significant coefficient sequence from the bitstream. Inoperation 406, the level information is recovered from the bitstreamusing entropy decoding. The significant coefficient sequence and levelinformation together are used to reconstruct the quantized transformdomain coefficient data in operation 408.

In one example implementation, the context for bins of the x-position(if it is the first to be encoded of the two-dimensional coordinates) isgiven by:

ctxIdxInc=binCtxOffset+binCtxInc

In this expression, ctxIdxInc is the context index for a given bin oflast_pos_x. The variable binCtxOffset is the context offset based uponthe transform size. In one embodiment the offset is determined inaccordance with the following table:

log2TrafoSize binCtxOffset 2 0 3 3 4 10 5 17

In this example, log 2TrafoSize is the binary logarithm of the transformmatrix size, i.e. log₂(N).

The other variable in the expression for context index above isbinCtxInc, which represents the context index increment applied basedupon the value of prior bins in last_pos_x, if any. The binCtxIncvariable may be determined, for example, in accordance with thefollowing table:

binIdx b₀ b₁ binCtxInc 0 na na 0 1 0 na 1 1 na 2 >=2 0 0 3 0 1 4 1 0 5 11 6

In this example, binIdx is the index of the bin in last_pos_x and b₀ andb₁ are bins in the last_pos_x binary sequence at index 0 and 1,respectively.

In one example embodiments, the context for bins of last_pos_y may bedetermined in accordance with the expression:

ctxIdxInc=binCtxOffset0+3*binCtxOffset1+binCtxInc

In this case, the context for a bin of last_pos_y depends upon the sizeof the transform matrix, prior bins of last_pos_y, if any, and upon thelast_pos_x value. Specifically, the transform matrix impacts contextthrough the variable binCtxOffset0, which may be determined inaccordance with the following table in some embodiments:

log2TrafoSize binCtxOffset0 2 0 3 9 4 21 5 35

The decoded bins of last_pos_y may impact context through the variablebinCtxInc, which may be determined in accordance with the followingtable in some embodiments:

binIdx b₀ binCtxInc 0 na 0 >=1 0 1 1 2

In this example, it will be noted that it is only the first bin at index0 that impacts context for any further bins of last_pos_y.

Finally, the value of last_pos_x may impact the context for a bin oflast_pos_y through the variable binCtxOffset1, which may be determinedby:

-   -   If last_pos_x==0

binCtxOffset1=0

-   -   Otherwise

binCtxOffset1=Floor(Log2(last_pos_x))+1

It will be appreciated that the foregoing example is but one exampleimplementation in which the context for bins of last_pos_y is dependentupon the value of last_pos_x. It will be understood that various otherimplementations may be realized with specific tables and context offsetsempirically designed to suit a particular application.

The meaning of the context index may be dependent upon the value of thequantization parameter (QP). That is, different contexts may be used tocode the same syntax with different QPs. Yet, these contexts may sharethe same context index. In one example embodiment, last_pos_x may becoded by Huffman codes. The corresponding Huffman trees may be dependentupon the value of QP. The contexts for coding bins of last_pos_x may bedependent upon the Huffman tree and thereby are different at differentQPs. For example, if one context is used for each QP, these contexts mayshare the same index 0 but have different meanings

In an alternative implementation, instead of encoding thetwo-dimensional Cartesian coordinates x and y, the last significantcoefficient position is represented by the anti-diagonal line that thecoefficient is on and the relative position of the coefficient on thatline. Reference is made to FIG. 11, which diagrammatically illustrates a4×4 block of coefficients 600. The anti-diagonal lines 602 are shown onthe block 600. It will be noted that there are seven anti-diagonallines, indexed as 0 to 6. Lines 0 and 6 have only a single position,which corresponds to x, y coordinates [0,0] and [3,3], respectively. Theother anti-diagonal lines 602 have between 2 and 4 positions each. Thepositions may be indexed in accordance with the conventions of thescanning order. That is, the indexing of the positions on theanti-diagonal lines may alternate from line-to-line in terms of theirdirections. Accordingly, the representation of each coordinate in a 4×4block may be expressed as an anti-diagonal-based two-dimensionalcoordinate, [a, b], as follows:

[0, 0] [1, 0] [2, 2] [3, 0] [1, 1] [2, 1] [3, 1] [4, 2] [2, 0] [3, 2][4, 1] [5, 0] [3, 3] [4, 0] [5, 1] [6, 0]

It will be noted that the last positions, [0,0] and [6,0], may beencoded by their anti-diagonal line number alone as there is no need tospecify the second coordinate for position on the line.

The [a, b] values may be encoded in a manner similar to that describedabove for two-dimensional coordinates x and y. The total number of codedbins for the anti-diagonal line index, a, is log₂(2N−-1). The number ofcoded bins for the position of the coefficient on the line, b, isdependent upon the value a, and is 1+log₂(a) for a<N and is1+log₂(2(N−1)−a) if a≧N. The context for encoding/decoding each bin isbased upon the value of the prior encoded/decoded bins.

In one other alternative implementation, rather than encoding atwo-dimensional coordinate for the last significant coefficientposition, the encoder encodes the 1-dimensional coordinate for the lastsignificant position having regard to the coefficient scanning order.The coefficient scanning order may be in the zig-zag order used inH.264, or in any adaptive or non-adaptive scanning order used in othertransform domain image or video encoding schemes. In thisimplementation, instead of last_pos _x and last_pos_y, the encoderencodes only last_pos, which ranges from 0 to (N*N−1), where N is thesize of the block of transform domain coefficients. The range forlast_pos need not include zero if the last_(—)0_flag is used in thesyntax. In some instances, last_pos may be automatically decremented,such that the decoder knows it must add 1 to the last_pos value torealize the actual 1-dimensional coordinate for the last significantcoefficient position.

The last_pos value may be encoded in a manner similar to that describedabove for one of the two-dimensional coordinates x. The total number ofcoded bins for the 1-dimensional coordinate, last_pos, is 2 log₂(N). Thecontext for encoding/decoding each bin is based upon the value of theprior encoded/decoded bins.

It should be noted that in the example implementations, the worst-casenumber of coded bins for the two-dimensional (or one-dimensional) lastsignificant coefficient position is in the order of log₂(N), which isfar less than N*N, the worst-case number of coded bins for theconventional last[i,j] sequences, thereby reducing the complexity inentropy coding engine implementation.

In yet a further aspect of the present application, it may beadvantageous to use the last position encoding process described aboveonly with certain blocks. In particular, the process may be moreadvantageous with block having more than a preset number ofcoefficients. Block that have few coefficients may be more efficientlyencoded using the conventional interleaved sig[i,j] and last[i,j] syntaxdescribed earlier. Accordingly, in one embodiment, the encoderdetermines the number of non-zero (NNZ) coefficients in a block andencodes the sig[i,j] and last[i,j] sequences using conventional syntaxif the NNZ is less than a threshold value. The threshold value may bepreset at 2, 3 or any other suitable value. If the NNZ is equal to orgreater than the threshold value, then the encoder uses thetwo-dimensional (or one-dimensional) last significant coefficientposition encoding process described above.

The syntax may be adapted to include a flag for signaling to the decoderwhether the NNZ coefficients for a block are less than a threshold valueor not. This also signals which significant map encoding process wasused by the encoder. In some instance, the last_(—)0_flag may beeliminated since the signaling of a DC only block is relativelyefficient in the conventional significance map encoding process.

Reference is now made to FIG. 10, which shows, in simplified flowdiagram form, a method 500 for encoding a significance map. The method500 is performed for each block of quantized transform domaincoefficients. It includes determining the NNZ coefficients in the blockin operation 502. In operation 504, the NNZ coefficients is compared toa preset threshold. If the NNZ coefficients is below the threshold, thenthe encoder uses conventional interleaved significance map encoding asindicated in operation 506. If the NNZ coefficients is equal to orgreater than the threshold value, then in operation 508 the encoderencodes the last position coordinates as described above.

It will be appreciated that the foregoing example methods areillustrations of a specific example application for encoding anddecoding significance maps, such as those prescribed in H.264. Thepresent application is not limited to that specific example application.

Reference now made to FIG. 4, which shows a simplified block diagram ofan example embodiment of an encoder 900. The encoder 900 includes aprocessor 902, memory 904, and an encoding application 906. The encodingapplication 906 may include a computer program or application stored inmemory 904 and containing instructions for configuring the processor 902to perform steps or operations such as those described herein. Forexample, the encoding application 906 may encode and output bitstreamsencoded in accordance with the last significant coefficient positionencoding process described herein. The encoding application 906 mayinclude an entropy encoder 26 configured to entropy encode inputsequences and output a bitstream using one or more of the processesdescribed herein. It will be understood that the encoding application906 may be stored in on a computer readable medium, such as a compactdisc, flash memory device, random access memory, hard drive, etc.

In some embodiments, the processor 902 in the encoder 900 may be asingle processing unit configured to implement the instructions of theencoding application 906. It will further be appreciated that in someinstances, some or all operations of the encoding application 906 andone or more processing units may be implemented by way ofapplication-specific integrated circuit (ASIC), etc.

Reference is now also made to FIG. 5, which shows a simplified blockdiagram of an example embodiment of a decoder 1000. The decoder 1000includes a processor 1002, a memory 1004, and a decoding application1006. The decoding application 1006 may include a computer program orapplication stored in memory 1004 and containing instructions forconfiguring the processor 1002 to perform steps or operations such asthose described herein. The decoding application 1006 may include anentropy decoder 1008 configured to receive a bitstream encoded inaccordance with the last significant coefficient position encodingprocess described herein, and to reconstruct quantized transform domaincoefficient data using the last significant coefficient position contextmodeling process for decoding the bitstream, as described herein. Itwill be understood that the decoding application 1006 may be stored inon a computer readable medium, such as a compact disc, flash memorydevice, random access memory, hard drive, etc.

In some embodiments, the processor 1002 in the decoder 1000 may be asingle processing unit configured to implement the instructions of thedecoding application 1006. In some other embodiments, the processor 1002may include more than one processing unit capable of executinginstructions in parallel. The multiple processing units may be logicallyor physically separate processing units. It will further be appreciatedthat in some instances, some or all operations of the decodingapplication 1006 and one or more processing units may be implemented byway of application-specific integrated circuit (ASIC), etc.

It will be appreciated that the decoder and/or encoder according to thepresent application may be implemented in a number of computing devices,including, without limitation, servers, suitably programmed generalpurpose computers, set-top television boxes, television broadcastequipment, and mobile devices. The decoder or encoder may be implementedby way of software containing instructions for configuring a processorto carry out the functions described herein. The software instructionsmay be stored on any suitable computer-readable memory, including CDs,RAM, ROM, Flash memory, etc.

It will be understood that the encoder and decoder described herein andthe module, routine, process, thread, or other software componentimplementing the described method/process for configuring the encodermay be realized using standard computer programming techniques andlanguages. The present application is not limited to particularprocessors, computer languages, computer programming conventions, datastructures, other such implementation details. Those skilled in the artwill recognize that the described processes may be implemented as a partof computer-executable code stored in volatile or non-volatile memory,as part of an application-specific integrated chip (ASIC), etc.

Certain adaptations and modifications of the described embodiments canbe made. Therefore, the above discussed embodiments are considered to beillustrative and not restrictive.

1. A method for encoding quantized transform domain coefficient dataincluding last significant coefficient information, the methodcomprising: binarizing each of two positions of two-dimensionalcoordinates of the last significant coefficient; determining a contextfor each bin of one of the positions; determining a context for each binof the other of the positions, wherein the context of each bin of theother of the positions is based, in part, upon said one of thepositions; and entropy encoding the binarized positions based upon thecontext determined for each of the bins of the binarized positions toproduce encoded data.
 2. The method claimed in claim 1, whereinbinarizing comprises encoding each of the two positions as a fixedlength binary code.
 3. The method claimed in claim 1, whereindetermining a context for each bin of the other of the positionsincludes calculating a context index that specifies the determinedcontext, and wherein the context index is calculated based upon said oneof the positions, a transform block size, and previous bins in the otherof the positions, if any.
 4. The method claimed in claim 1, wherein thetwo positions comprise an x-position and a y-position within a block. 5.The method claimed in claim 1, wherein determining a context for eachbin of the other of the positions includes calculating a context indexthat specifies the determined context, wherein the context index isbased upon a binary logarithm of said one of the positions.
 6. Themethod claimed in claim 1, further comprising: determining that thetwo-dimensional coordinates are not [0,0] before performing saidbinarizing, determining the context for each bin of each position, andentropy encoding.
 7. The method claimed in claim 1, further comprisingcounting a number of non-zero coefficients in the quantized transformdomain coefficient data and determining that the number meets or exceedsa threshold before said binarizing, said determining a context for eachbin of one of the positions and said determining a context for each binof the other of the positions.
 8. An encoder for encoding quantizedtransform domain coefficient data, the encoder comprising: a processor;a memory; and an encoding application stored in memory and containinginstructions for configuring the processor to binarize each of twopositions of two-dimensional coordinates of the last significantcoefficient; determine a context for each bin of one of the positions;determine a context for each bin of the other of the positions, whereinthe context of each bin of the other of the positions is based, in part,upon said one of the positions; and entropy encode the binarizedpositions based upon the context determined for each of the bins of thebinarized positions to produce encoded data.
 9. The encoder claimed inclaim 8, wherein the processor is configured to binarize by encodingeach of the two positions as a fixed length binary code.
 10. The encoderclaimed in claim 8, wherein the processor is configured to determining acontext for each bin of the other of the positions by calculating acontext index that specifies the determined context, and wherein thecontext index is calculated based upon said one of the positions, atransform block size, and previous bins in the other of the positions,if any.
 11. The encoder claimed in claim 8, wherein the two positionscomprise an x-position and a y-position within a block.
 12. The encoderclaimed in claim 8, wherein the processor is configured to determine acontext for each bin of the other of the positions by calculating acontext index that specifies the determined context, wherein the contextindex is based upon a binary logarithm of said one of the positions. 13.The encoder claimed in claim 8, wherein the processor is configured todetermine that the two-dimensional coordinates are not [0,0] beforeperforming said binarizing, determining the context for each bin of eachposition, and entropy encoding.
 14. The encoder claimed in claim 8,wherein the processor is configured to count a number of non-zerocoefficients in the quantized transform domain coefficient data anddetermine that the number meets or exceeds a threshold before saidbinarizing, said determining a context for each bin of one of thepositions and said determining a context for each bin of the other ofthe positions.
 15. A method for decoding a bitstream of encoded data toreconstruct quantized transform domain coefficient data, the methodcomprising: entropy decoding a portion of the encoded data to producetwo binarized positions defining two-dimensional coordinates of a lastsignificant coefficient, wherein entropy decoding the portion of thedata includes determining a context for each bin of one of thepositions, and determining a context for each bin of the other of thepositions, wherein the context of each bin of the other of the positionsis based, in part, upon said one of the positions; entropy decoding asignificant coefficient sequence based upon the two-dimensionalcoordinates of the last significant coefficient; entropy decoding levelinformation based upon the significant coefficient sequence; andreconstructing the quantized transform domain coefficient data using thelevel information and the significant coefficient sequence.
 16. Themethod claimed in claim 15, wherein the two binarized positions eachcomprise a fixed-length binary code.
 17. The method claimed in claim 15,wherein entropy decoding the significant coefficient sequence includesconverting the two-dimensional coordinates of the last significantcoefficient to a one-dimensional index indicating the end of thesignificant coefficient sequence.
 18. The method claimed in claim 15,wherein determining a context for each bin of the other of the positionsincludes calculating a context index that specifies the determinedcontext, and wherein the context index is calculated based upon said oneof the positions, a transform block size, and previous bins in saidother of the positions, if any.
 19. The method claimed in claim 15,wherein the two positions comprises an x-position and a y-positionwithin a block.
 20. The method claimed in claim 15, wherein determininga context for each bin of the other of the positions includescalculating a context index that specifies the determined context,wherein the context index is based upon a binary logarithm of said oneof the positions.
 21. The method claimed in claim 15, further comprisingentropy decoding a zero flag and determining from the zero flag that thetwo-dimensional coordinate position is not [0,0] before decoding saidportion.
 22. The method claimed in claim 15, further comprising entropydecoding a non-zero coefficient flag and, based on the value of thenon-zero coefficient flag, performing said entropy decoding a portion.23. A decoder for decoding a bitstream of encoded data to reconstruct asequence of symbols, the symbols belonging to a finite alphabet, thedecoder comprising: a processor; a memory; and a decoding applicationstored in memory and containing instructions for configuring theprocessor to entropy decode a portion of the encoded data to produce twobinarized positions defining two-dimensional coordinates of a lastsignificant coefficient, wherein entropy decoding the portion of thedata includes determining a context for each bin of one of thepositions, and determining a context for each bin of the other of thepositions, wherein the context of each bin of the other of the positionsis based, in part, upon said one of the positions; entropy decode asignificant coefficient sequence based upon the two-dimensionalcoordinates of the last significant coefficient; entropy decode levelinformation based upon the significant coefficient sequence; andreconstruct the quantized transform domain coefficient data using thelevel information and the significant coefficient sequence.
 24. Thedecoder claimed in claim 23, wherein the two binarized positions eachcomprise a fixed-length binary code.
 25. The decoder claimed in claim23, wherein the processor is configured to entropy decode thesignificant coefficient sequence by converting the two-dimensionalcoordinates of the last significant coefficient to a one-dimensionalindex indicating the end of the significant coefficient sequence. 26.The decoder claimed in claim 23, wherein the processor is configured todetermine a context for each bin of the other of the positions bycalculating a context index that specifies the determined context, andwherein the context index is calculated based upon said one of thepositions, a transform block size, and previous bins in said other ofthe positions, if any.
 27. The decoder claimed in claim 23, wherein thetwo positions comprises an x-position and a y-position within a block.28. The decoder claimed in claim 23, wherein the processor is configuredto determine a context for each bin of the other of the positions bycalculating a context index that specifies the determined context,wherein the context index is based upon a binary logarithm of said oneof the positions.
 29. The decoder claimed in claim 23, wherein theprocessor is configured to entropy decode a zero flag and determiningfrom the zero flag that the two-dimensional coordinate position is not[0,0] before decoding said portion.
 30. The decoder claimed in claim 23,wherein the processor is configured to entropy decode a non-zerocoefficient flag and, based on the value of the non-zero coefficientflag, performing said entropy decoding a portion.
 31. Acomputer-readable medium having stored thereon computer-executableinstructions which, when executed by a processor, configure theprocessor to execute the method claimed in claim 1.